Derivation of Geometrically Parameterized Shell Elements in the Context of Shape Optimization

The goal of this contribution is to extend an existing workflow for shape optimization with geometrically parameterized finite elements by implementing a parameterized shell element. The challenge is to find an element technology that is free of locking and hourglass-modes on the one hand, but its implementation must be simple enough so that it can contain the geometric parameters on the other hand. The derived element is used in a numerical optimization example. Therefore, a ribbed plate is used to show the whole workflow including the preparation of the system matrices depending on global design parameters, parametric model order reduction and shape optimization. A final validation is done using a commercial finite element software to compare the results.